Finite Group Databasebeta

← C2×C5×D5×C3⋊D3 #14268533

Subgroups — C2×C5×D5×C3⋊D3 #14268533

Order 1800.

444 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C3⋊D15C211yesmaximal, characteristic, complemented
2C2×C52×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C32×C5×D5C211yesmaximal, characteristic, complemented
4C5×D5×C3⋊D3C214yesmaximal, direct product factor
5C2×C5×D3×D5—34nomaximal
6C2×C32×C52C2211yescharacteristic, complemented
7C5×C3⋊D15C2212yescomplemented
8C52×C3⋊D3C2212yescomplemented
9C32×C5×D5C2212yescomplemented
10C22×C5×C3⋊D3—51nomaximal
11C2×D5×C3⋊D3C511yesmaximal, characteristic, direct product factor
12C2×C5×D15—34no—
13C2×C52×D3—34no—
14C2×C3×C5×D5D314yescomplemented
15C5×D3×D5—316no—
16C32×C52C2311yescharacteristic, complemented, Hall
17C22×C5×D5—91noHall
18C22×C32×C5—51no—
19C2×C3⋊D15C2×C511yescharacteristic, complemented
20C2×C5×C3⋊D3—22no—
21C2×C5×C3⋊D3—51no—
22C2×C5×C3⋊D3—54no—
23C2×C5×C3⋊D3D511yescharacteristic, direct product factor
24C2×C5×C3⋊D3C2×C511yescharacteristic, complemented
25C2×C32×D5C2×C511yescharacteristic, complemented
26D5×C3⋊D3C2×C514yesdirect product factor
27C2×C3×C52C2×D314yescomplemented
28C5×D15—38no—
29C52×D3—38no—
30C3×C5×D5C2×D318yescomplemented
31C22×C5×D3—154no—
32C2×D3×D5—34no—
33C22×C52—91no—
34C2×C5×D5—94no—
35C2×C5×D5—91no—
36C2×C5×D5C3⋊D311yescharacteristic, direct product factor
37C2×C32×C5—22no—
38C2×C32×C5—52no—
39C2×C32×C5C2×D511yescharacteristic, complemented
40C2×C32×C5C22×C511yescharacteristic, complemented
41C3⋊D15C22×C512yescomplemented
42C5×C3⋊D3—24no—
43C5×C3⋊D3—52no—
44C5×C3⋊D3C2×D512yesdirect product factor
45C5×C3⋊D3C22×C512yescomplemented
46C32×D5C22×C512yescomplemented
47C3×C52C22×D314yescomplemented
48C22×C3⋊D3—51noHall
49C22×C3×C5—54no—
50C2×D15—34no—
51C2×C5×D3—34no—
52C2×C5×D3—34no—
53C2×C5×D3—68no—
54C2×C5×D3—1516no—
55C2×C5×D3—154no—
56C2×C3×D5C5×D314yescomplemented
57D3×D5—316no—
58C2×C52—92no—
59C2×C52C2×C3⋊D311yescharacteristic, complemented
60C5×D5—92no—
61C5×D5C2×C3⋊D312yesdirect product factor
62C32×C5—22no—
63C32×C5C22×D511yescharacteristic, complemented
64C32×C5C23×C511yescharacteristic, complemented
65C23×C5—451no—
66C22×D5—91no—
67C22×C32—51no—
68C2×C3⋊D3—51no—
69C2×C3⋊D3—54no—
70C2×C3⋊D3C5×D511yescharacteristic, direct product factor
71C2×C3×C5—28no—
72C2×C3×C5—58no—
73C2×C3×C5D3×D514yescomplemented
74C2×C3×C5C2×C5×D314yescomplemented
75D15—38no—
76C3×D5C2×C5×D318yescomplemented
77C5×D3—38no—
78C5×D3—38no—
79C5×D3—616no—
80C5×D3—158no—
81C52C22×C3⋊D311yescharacteristic, complemented, Sylow
82C22×D3—154no—
83C22×C5—51no—
84C22×C5—91no—
85C22×C5—91no—
86C22×C5—182no—
87C22×C5—454no—
88C22×C5—451no—
89C2×D5—91no—
90C2×D5—94no—
91C2×D5C5×C3⋊D311yescharacteristic, direct product factor
92C2×C32—52no—
93C2×C32C2×C5×D511yescharacteristic, complemented
94C3⋊D3—52no—
95C3⋊D3C2×C5×D512yesdirect product factor
96C3×C5—28no—
97C3×C5C2×D3×D514yescomplemented
98C3×C5C22×C5×D314yescomplemented
99C22×C3—54no—
100C2×D3—34no—
101C2×D3—1516no—
102C2×D3—154no—
103C2×C5—22no—
104C2×C5—52no—
105C2×C5—92no—
106C2×C5—92no—
107C2×C5—184no—
108C2×C5—452no—
109C2×C5D5×C3⋊D311yescharacteristic, direct product factor
110C2×C5C2×C5×C3⋊D311yescharacteristic, complemented
111D5—92no—
112D5C2×C5×C3⋊D312yesdirect product factor
113C32C22×C5×D511yescharacteristic, complemented, Sylow
114C23—451noSylow
115C2×C3—58no—
116C2×C3C5×D3×D514yescomplemented
117D3—38no—
118D3—158no—
119C5—22no—
120C5C2×D5×C3⋊D311yescharacteristic, direct product factor
121C5C22×C5×C3⋊D311yescharacteristic, complemented
122C22—51no—
123C22—91no—
124C22—454no—
125C22—451no—
126C3C2×C5×D3×D514yescomplemented
127C2—52no—
128C2—92no—
129C2—452no—
130C2C5×D5×C3⋊D311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5D5×C3⋊D3
commutator, cosocle, hypocenterC32×C5C23×C5
FrattiniC1G
Fitting, socleC2×C32×C52C22
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C5×C3⋊D15C2semidirect
2. C2×C52×C3⋊D3C2semidirect
3. C2×C32×C5×D5C2semidirect
4. C5×D5×C3⋊D3C2direct (N × H)
6. C2×C32×C52C22semidirect
7. C5×C3⋊D15C22semidirect
8. C52×C3⋊D3C22semidirect
9. C32×C5×D5C22semidirect
11. C2×D5×C3⋊D3C5direct (N × H)
14. C2×C3×C5×D5D3semidirect
16. C32×C52C23semidirect
19. C2×C3⋊D15C2×C5semidirect
23. C2×C5×C3⋊D3D5direct (N × H)
24. C2×C5×C3⋊D3C2×C5semidirect
25. C2×C32×D5C2×C5semidirect
26. D5×C3⋊D3C2×C5direct (N × H)
27. C2×C3×C52C2×D3semidirect
30. C3×C5×D5C2×D3semidirect
36. C2×C5×D5C3⋊D3direct (N × H)
39. C2×C32×C5C2×D5semidirect
40. C2×C32×C5C22×C5semidirect
41. C3⋊D15C22×C5semidirect
44. C5×C3⋊D3C2×D5direct (N × H)
45. C5×C3⋊D3C22×C5semidirect
46. C32×D5C22×C5semidirect
47. C3×C52C22×D3semidirect
56. C2×C3×D5C5×D3semidirect
59. C2×C52C2×C3⋊D3semidirect
61. C5×D5C2×C3⋊D3direct (N × H)
63. C32×C5C22×D5semidirect
64. C32×C5C23×C5semidirect
70. C2×C3⋊D3C5×D5direct (N × H)
73. C2×C3×C5D3×D5semidirect
74. C2×C3×C5C2×C5×D3semidirect
76. C3×D5C2×C5×D3semidirect
81. C52C22×C3⋊D3semidirect
91. C2×D5C5×C3⋊D3direct (N × H)
93. C2×C32C2×C5×D5semidirect
95. C3⋊D3C2×C5×D5direct (N × H)
97. C3×C5C2×D3×D5semidirect
98. C3×C5C22×C5×D3semidirect
109. C2×C5D5×C3⋊D3direct (N × H)
110. C2×C5C2×C5×C3⋊D3semidirect
112. D5C2×C5×C3⋊D3direct (N × H)
113. C32C22×C5×D5semidirect
116. C2×C3C5×D3×D5semidirect
120. C5C2×D5×C3⋊D3direct (N × H)
121. C5C22×C5×C3⋊D3semidirect
126. C3C2×C5×D3×D5semidirect
130. C2C5×D5×C3⋊D3direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C5×C3⋊D152
C2×C52×C3⋊D32
C2×C32×C5×D52
C5×D5×C3⋊D32
C2×C5×D3×D53
C22×C5×C3⋊D35
C2×D5×C3⋊D35